The divisiveness is a consequence of the primary system, not the two-party system. The primary system is very new, only here since 1972, but the fact is that 1) the power to nominate candidates should have never been handed to the voters, and 2) now that it has been, it is impossible to revoke. The "strategic" aspect of nominating a candidate closer to the center, to capture as much of the political spectrum as possible, is impossible to coordinate with individual voters but very easy to execute by party insiders.

Without primaries, Barack Obama would have never been President but Donald Trump wouldn't have been either.